Using Transmissive Photonic Band Edge Shift to Detect Explosives: A

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Using Transmissive Photonic Band Edge Shift to Detect Explosives – A Study with 2,4,6-trinitrotolune (TNT) Noorhayati Idros, Man Yi Ho, Varun S Kamboj, Hua Xu, Zhongze Gu, Harvey E Beere, David A. Ritchie, and Daping Chu ACS Photonics, Just Accepted Manuscript • DOI: 10.1021/acsphotonics.6b00880 • Publication Date (Web): 20 Jan 2017 Downloaded from http://pubs.acs.org on January 23, 2017

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Using Transmissive Photonic Band Edge Shift to Detect Explosives – A Study with 2,4,6-trinitrotolune (TNT) Noorhayati Idros 1,2 , Man Yi Ho 1,3 , Varun S. Kamboj Harvey E. Beere 4 , David A. Ritchie 4 , Daping Chu 1* 1

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3

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, Hua Xu

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, ZhongZe Gu

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Electrical Engineering Division, Engineering Department, University of Cambridge, Cambridge, CB3 0FA, United Kingdom. Institute of Nano Electronic Engineering (INEE), Universiti Malaysia Perlis (UniMAP), Lot 106, 108 & 110, Tingkat 1, Block A, Taman Pertiwi Indah, Jalan Kangar-Alor Setar, Seriab 01000 Kangar, Perlis, Malaysia. Schlumberger Cambridge Research, High Cross, Madingley Road, Cambridge, CB3 0EL, United Kingdom. Cavendish Laboratory, Physics Department, University of Cambridge, Cambridge, CB3 0HE, United Kingdom. State Key Laboratory of Bioelectronics, School of Biological Science and Medical Engineering, Southeast University, 2 Sipailou, Nanjing, 210096, China.

Corresponding Author * Author to whom correspondence should be addressed; E-Mail: [email protected]; Tel.: +44 (0) 1223 748352; Fax: +44 (0) 1223 748342 ABSTRACT Photonic crystals (PhCs) possess outstanding optical properties that can be exploited for chemical sensing. We utilized a three-dimensional close-packed PhC structure made of functionalized silica nanoparticles. They consist of alternating high and low refractive index regions and has optical properties, such as photonic band structures, that are very sensitive to the change of physical structures. This study use 2,4,6-trinitrotolune (TNT) to illustrate a detection method based on the transmissive photonic band edge shift (TPBES) due to the binding of TNT with amine anchored on particle surfaces to form Meisenheimer (amine-TNT) complexes. PhCs are exceptionally sensitive to a small change in refractive index caused by surface modification. As a result, it is suitable for sensing specific reactions between amine and TNT. This method achieved a wide detection range of TNT concentrations from 10-12 M to 10-4 M. 2,4-dinitritoluene (DNT) and toluene were used as a control and blank, respectively. Because of gravitational sedimentation, the TNT-functionalized particles were self-assembled in pure ethanol. They were measured by UV-Visible transmission spectroscopy. A three-dimensional model to simulate the detection system was built using the particles centre-to-centre distance (a) and effective dielectric constant (ε) as a function of the TNT concentrations. Two sets of simulations were performed: the first set involved a parametric sweep of the centre-to-centre distance of TNT functionalized crystals using ε = 2.015. The second set involved a parametric sweep of the dielectric constant with a = 263.1 nm. These perturbations yield a TPBES response that is in agreement with our experimental results. KEYWORDS: Transmission, photonic crystal, nano particles, self-assembly, TNT

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Photonic crystals (PhCs) are periodic arrangements of regularly shaped materials with different dielectric constants.1 The material is engineered such that only light of a certain wavelength can propagate through the lattice of this arrangement.2 Yablonovitch and John undertook the first detailed research on engineered PhCs.3-4 The periodicity of PhCs can vary from a single-dimensional (1D) to a three-dimensional (3D) structure depending on its applications. Fabrication of 1D and 2D PhCs are mostly prepared by conventional lithography techniques such as photolithography, multiple spin coating, layer-by-layer deposition, and etching.5-8 3D PhCs however, can be produced by cheaper techniques such as self-assembly of nanoscopic, monodisperse spheres into a photonic crystal host simply known as colloidal selfassembly.9-10 Normally such spheres consist of dielectric materials, for example, silica, titanium dioxide, zinc oxide, or organic polymers including poly(methyl methacrylate) and polystyrene.1118

Colloidal self-assembly offers a means of low-cost production of 3D photonic crystals with a

large surface area19-20 and which exhibit a complete photonic bandgap. The combination of these two factors enables these crystals to manipulate light in 3D space.10 Photonic bandgaps (PBGs) forbid propagation of electromagnetic waves of certain frequency ranges. The optical properties of PBG structures are highly sensitive to the thickness and refractive index of their constituents. Small changes in the refractive index of PBG structures due to the capturing of external stimuli1 such as a ligand-receptor interaction can be detected as shifts in the reflectance spectrum.21 Colloidal mesoporous such as silica nanoparticles have several benefits: they offer a large sensing surface area; they available to integrate functional groups; and they are capable of immobilizing into an inorganic mesopores network with active molecules.22–29 In addition, the mesoporous particles in suspension can stay suspended over a long period of time, making them ideal for surface coatings.30 Colloidal mesoporous nanoparticles have found promising applications in the fluorogenic detection of nitroaromatic explosives such as luminescent colloidal oligo(tetraphenyl)silole nanoparticles in THF/H2O suspensions31, nanoscopic-capped mesoporous hybrid materials or MCM-41 support32, and silica mesoporous supports gated with tetrathiafulvalene derivatives.33 Xu and Lu34 developed a M-MIPs@CDs fluorescence sensor for detection of 2,4,6-trinitrotoluene (TNT) with sensitivity of 17 nM. Liu and Chen35 also reported detection of TNT with sensitivity of 10-11 M using graphene nanosheet-supported silver


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nanoparticles. The reported fluorescence sensors involved complex analytical instrumentations and expensive materials. However, in this proposed transmissive photonic band edge shift (TPBES) based detection of TNT offers an attractive option for a much simpler, inexpensive, convenient and label-free alternative1 with excellent sensitivity of pM. Sensing of trace explosives such as TNT is a complex and challenging task due to the lack of inexpensive sensors with high selectivity and sensitivity36, the lack of easily detectable signals, and wide selection of explosive compositions.37,38 Furthermore, explosive-based terrorism has grown rapidly in recent years, causing enormous damage to public safety and environmental pollution. These explosive-based weapons can be deployed in simple and variety of schemes. 39-41 Primarily used nitroaromatic explosives produced during military preparation of landmines42-47, TNT is also one of the key sources of dangerous water contamination,48 as well as being toxic to aquatic creatures. Exposure to TNT may cause pancytopenia, a disorder of the blood-forming tissues in humans and other mammals.49 Thus, developing a practical analytical method to monitor TNT is pressing and crucial to solving these problems. We propose a method to detect TNT by anchoring the SiO2 nanoparticles surface with amine (—NH2) head groups from 3-aminopropyl-triethoxysilane (APTES) that act as bioreceptors that selectively bind with TNT targets. This method is very selective and simpler than the two-step reactions reported in our previous findings50 since we have confirmed that APTES has an excellent selectivity with TNT. The formation of the amine-TNT or Meisenheimer complexes is attributed to the strong acceptor-donor interaction between the nitro group of TNT and amine respectively.51.52 Figure 1 shows the molecular schematic of the complex. Meisenheimer complex (amine-TNT)

(a)

(b)

O N+

O-

N+

O-

-

O N+ O +H

2N

O

O

Si

Si

OO O O

O

HO

Figure 1. Molecular schematic of the Meisenheimer complex: (a) Ball and stick threedimensional representation. The 3D structure represents oxygen, hydrogen, nitro, carbon and


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silicon atoms as red, white, blue, gray and purple balls respectively. (b) Chemical structure representation of the Meisenheimer (amine-TNT) complex functionalized onto the SiO2 crystal.

The surface functionalization scheme is demonstrated in Figure 2. As a result of ligands binding, the nanoparticle separation increased from state 1 to 3 (a0 to a2). An increase in the TNT concentrations further increase the effective particle separation and the contrast of the refractive index of the functionalized system.

Figure 2. Surface functionalization of silica particles: the separation between the close-packed particles increases from state 1 to 3 (a0 to a2).

Self-assembly of the functionalized nanoparticles forms a closely-packed structure that can be observed under scanning electron microscopy. Because of gravitational sedimentation, the TNT-functionalized particles were self-assembled in pure ethanol. This sedimentation structure is shown in Figure 3. The settled structure was measured by UV-Visible transmission spectroscopy. From the measurement, three regions of high and low transmittance were observed. The high and low transmittance edges are the respective photonic band (PB) and band gap (PBG) edges.


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Figure 3: Self-assembled structure of functionalized TNT particles under gravity force. TPBES response measures the normalized frequency calculated as the particles centre-tocentre distance (a) divided by the measured wavelength (λ), as a function of TNT concentrations. A wide detection range of TNT concentrations was used and successfully detected from 10-12 M to 10-4 M together with 2,4-dinitritoluene (DNT) and toluene as control and blank, respectively. The TPBES system is very selective towards TNT even though the chemical structure of TNT and DNT are relatively similar as shown in Figure 4. Apart from the outstanding selectivity between amine and TNT, the effective particle separation (a) increased with the TNT concentration and changed the contrast of the refractive index (neff) which resulted in the PB and PBG edge shifts. Successful detection of TNT is caused by a periodic arrangement of the functionalized crystals. On the other hand, an incomplete reaction between DNT and amine resulted in randomization of their self-assembly structure. This randomization effect resulted in decreasing signals of TPBES response with no distinctive photonic bands and band gaps shown in the results section. O

(a)

-

CH3

O N

N O

CH3

(b)

+

+

O

+

N

-

O

+

O

-

O -

+

N

O

O

-

N

O

Figure 4: Explosive structures of (a) TNT and (b) DNT.

A three-dimensional model to simulate the detection system was built using the particles centre-to-centre distance (a) and effective dielectric constant (ε) as a function of the TNT concentrations. Two sets of simulations were performed: the first set involved a parametric


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sweep of the centre-to-centre distance of TNT functionalized crystals using ε = 2.015; the second set involved a parametric sweep of the dielectric constant with a = 263.1 nm. The perturbations of the centre-to-centre distance and dielectric constant yield a TPBES response as described by Equation (i) in the result section. We observed that the simulation results are in agreement with our experimental results that are further described in the results section. This detection method reveals band edges sharper than reported in our previous findings50 with full penetration of light through the three-dimensional self-assembly structure. A combined effect of the high surface area-to-volume ratio of the functionalized nano particles in use and the full penetration of the light through the assembled structure, helped to expand the dynamic range of the detection from 10-12 to 10-4 M. The method presented in this study offers a convenient tool for label-free sensing, since the effect can be made specific for TNT, and can be incorporated easily into microfluidic systems.

Results Transmissive Photonic Band Edge Shift. The transmission spectrums for bare silica and amine-functionalized crystals are illustrated in Figure 5 (a) (i) and (ii), respectively. They exhibit sharp band edges which consist of three high and low regions that correspond to respective photonic band and band gaps. A photonic band edges are the edges of the high normalized frequencies, calculated as the particles centre-to-centre distance (a) divided by the measured wavelength (λ). The shifts in the photonic bands (PBs) and band gaps (PBGs) for bare silica and amine-functionalized crystals are plotted in Figure 5 (b). The shift is caused by an increased in the average centre-to-centre distance (a) from 250.2 nm to 257.7 nm, measured by scanning electron microscopy (SEM). Sampling on the transmission of 10-4 M TNT as seen in Figure 5 (c) exhibits sharper edges in comparison to the reflection signal and other TNT-detection configurations30, 53-58. These edges provide an accurate indication of the bands with small measurement error in the whole composition range. From an applied standpoint, TPBES response offers a better detection system than its counterpart for of the following reasons. Firstly, the reflection technique is limited only to the light interaction on the crystals surface than the overall three-dimensional penetration of the assembled structure seen by the transmitted lights.


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Secondly, the arrangement of packed crystals from the gravity sedimentation method59-60 used to grow the reflection films is restricted by their low mobility on the bottom substrate when the gravity force surpasses the Brownian motion or interparticle electrostatic repulsion. Thus, the resultant self-assembled crystals are considerably less ordered, and they exhibit poor assembly efficiency in particularly on the surface. Cracks regularly occur upon drying due to the tensile stress arising from the capillary-force-induced shrinkage of the pre-assembled array against a rigid substrate61.

Photonic Band

(b)

Photonic Band gap

(ii) −NH2-SiO2 0.8

0.6

(i) SiO 2

0.4

0.2 0.3

0.4 0.5 0.6 Normalized Frequency (a/λ)

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0.7

SiO2 (PB) −NH2-SiO2 (PBG) −NH2-SiO2 (PB)

0.6

0.6

0.5

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10-4 M TNT

(c)

SiO2 (PBG)

0.7 Photonic Band (a/λ)

Normalized Transmission

1.0

E1'

E2 E2' Band edges

E3

E3'

(d)

2.00

Photonic Band

1.20

1.84

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1.76

0.40

1.68 4x decrease

0.00 0.3

1.60 0.4

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1.92 4x increase


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(a)

Normalized Reflection

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Photonic Band gap

0.8 0.6 TNT

0.4 0.2

DNT

0.0 0.4

0.6

0.8

1.0

1.2

Normalized Frequency (a/λ)

Figure 5. Transmissive Photonic Band Edge Shift: (a) Normalized transmission against normalized frequency (a/λ) of (i) SiO2 and (ii) —NH2-SiO2. (b) The corresponding TPBES response of photonic band and band gap edges before and after amine functionalization. (c) For the sake of contrast, sampling on the normalized reflection (with signal decreased by four times) exhibit edges less sharp in comparison to the normalized transmission (with signal increased by four times). (d) The TPBES responses of 10-4 M TNT and DNT functionalized crystals.


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TPBES crystals assembled in solution achieve equilibrium between stabilizing and destabilizing factors of gravity, of the respective Brownian motion and interparticle forces. Due to these reasons, the structure of the TPBES crystals may have higher regularity as a whole than the structure obtained in the reflection side. The increase of TNT concentrations from 10-12 M to 10-4 M further increased the effective particle separation as shown in Table 1. This is because successful detection of TNT on the amine-functionalized crystals (—NH2-SiO2) surfaces resulted in a periodic arrangement of the functionalized crystals. Figure 6 (a) and (b) are the SEM images of the respective structures of —NH2-SiO2 and 10-4 M TNT-functionalized crystals. The centre-to-centre distance of crystals increased from 257.7 nm of the —NH2-SiO2 to 270.9 nm after 10-4 M TNT functionalization. Table 1. Average center-to-center distance, (a) of functionalized crystals measured by scanning electron microscopy for different TNT concentrations. Concentration of TNT (M) 10-12 10-10 10-8 10-6 10-4

Centre-to-centre distance (nm) 263.1 265.4 266.0 267.2 270.9

An incomplete reaction between DNT and —NH2-SiO2 crystals50 resulted in randomization of their self-assembly structures as shown in Figure 6 (c). Using SEM measured only on uniform crystal areas, the centre-to-centre distance of the 10-4 M DNT-crystals is approximated to be 286 nm. However, this value does not represent the entire sample because of the randomization effect. The randomization of DNT crystals resulted in decreasing signals of its TPBES response shown in Figure 5 (d) with no distinctive photonic bands and band gaps. The approximated centre-to-centre distance of the DNT-crystals was used in order to compare the TPBES response between 10-4 M TNT- and the control DNT-functionalized crystals.


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Crystal structures nonetheless, remain unchanged after incubation of aminefunctionalized silica with a blank compound, toluene. TNT functionalization therefore, produced organized structures, while the control DNT produced randomized structures and toluene have no functionalization effect on the —NH2-SiO2 crystals. The photonic band and band gaps of both the transmission and reflection spectrums from the studied detection range are plotted in Figure 7 (a) and (b), respectively. In these plots, control DNT has zero band edges because of the impossibility of measuring their centre-to-centre distance due to the randomization effect. Higher band edges are labeled as Em’ with m = 1,2,3. From the response curves, PB and PBG edges increased with the increasing TNT concentration.

(a)

DNT (control)

TNT

(c)

(b)

Figure 6. Scanning electron microscopy (SEM) images of (a) amine-functionalized silica (— NH2-SiO2) crystals, (b) 10-4 M TNT- and (c) 10-4 M DNT-functionalized on the —NH2-SiO2 surfaces.


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A third order polynomial fit was used to extract the , , and slope values following the

fitting equation: = + . + . + . , where is the intercept, , , are the slopes. Table 4 shows a list of the fitting parameters in the method section.

Figure 7 shows a monotonic TPBES responses as a function of the TNT concentration. In contrast to the TPBES response, it is evident that the reflection band edges possess larger error bars due to its ‘dull’ edges. Since the band edges of the TPBES response behave monotonically, its first order slope, α for both photonic bands and band gaps can be plotted as shown in Figure 8. This is a merit function of the TPBES detection system which proved to be more sensitive than the reflection technique for the same detection range. (i)

E1' E1' E1

0.4

E1

0.3 0.0 -0.1 10-14

DNT

10-12

10-10

10-8

10-6

10-4

0.3 0.0 -0.1

10-2

Photonic Bandgap E1' E1' E1

0.4

0.3 0.0 -0.1 10-14

10-12

Concentration of TNT (M)

10-10

10-8

(ii)

(ii)

Photonic Band

Photonic Bandgap

0.6

0.6 E2' E2'

0.5

E2 E2

0.4 0.0 -0.1 10-14

DNT

10-12

10-10

10-8

10-6

10-4

0.4 0.0 -0.1

10-2

0.7 Normalized Transmission

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0.4

DNT

0.3 0.0 -0.1

10-4

10-2

0.7 E2'

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0.6 E2' E2

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0.4 0.0 -0.1 10-14

10-12


(iii)

10-6

E1



0.7

0.5

10-10

10-8

10-6

E2

0.5

DNT

0.4 0.0 -0.1

10-4


0.4

0.5 Normalized Transmission

0.5


Photonic Band

(i)



0.5


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10-2

Concentration (M)

(iii)


10

0.9 Photonic Band 0.8

0.8 E3'

0.7

0.7 E3

0.6

0.6

E3' E3

0.5

0.5

0.4 0.0 -0.1 10-14

DNT

10-12

10-10

10-8

10-6

10-4

0.9

0.4 0.0 -0.1

10-2


0.9 Normalized Reflection


Photonic Bandgap

0.9

0.8

E3' E3

0.7

0.8 0.7

E3'

0.6

E3

0.5

0.6 0.5

0.4 0.0 -0.1 10-14


DNT

10-12

10-10

10-8

10-6

10-4

0.4 0.0 -0.1

10-2


(a)

(b)

Figure 7: Experimental results of the TPBES response (normalized transmission) and reflection as a function of TNT concentration: (a) photonic band and (b) band gap edges. slope = α

0.050 0.045

0.044

0.040 0.042

0.035 0.030

0.040

0.025 0.038

0.020 0.015

0.036

0.010 0.034

0.005

E1

E1'

E2

E2'

E3

Photonic Bandgap (α α (a/λ λ .M)

0.046

Photonic Band (α α (a/λ λ .M)

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E3'

Band edges

Figure 8. First-order slope, of photonic band and band gap from third order polynomial fit. The crystals centre-to-centre distance after TNT functionalization was also examined in solution using a well-established technique known as Zetasizer Nano-ZS, a tool based on dynamic light scattering (DLS). Results of the DLS Intensity Mean (d.nm) measurement of the TNT-functionalized crystals at different concentrations is shown in Figure 9. DLS findings validate their agreement with the SEM results.


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285

285 DLS SEM

280

280

275

275

270

270

265

265 Baseline

260 255

260 255

Baseline

250 10-14

10-12 10-10 10-8 10-6 10-4 Concentration of TNT (M)

250 10-2

SEM (Centre-to-Centre Distance (nm))

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

DLS (Intensity Mean (d. nm))

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Figure 9. Dynamic light scattering (DLS) and scanning electron microscopy (SEM) results for different TNT concentrations. Toluene blank was used as the baseline for both measurements. Correlation between (a) and neff. The effective refractive index, neff depends on the centre-tocentre distance changed based on Equation (1) to (4) in the methods section. The neff of functionalized crystals in each functionalization state were calculated and are listed in Table 2. Although there is an increased in the centre-to-centre distance of 7.5 nm after amine functionalization, the neff remained the same as the bare silica. This is because amine functionalization caused decreased in the silica volume fraction from 52.4% to 47.9% to allow the 4.5% volume fraction of amine, within 47.6% volume fraction of ethanol. Based on Equation (1) and an analogous refractive index value for silica and amine of 1.46, resulted in an analogous ε as shown in Table 2.

Table 2. The effective refractive indices neff, and their corresponding dielectric constant, ε for bare and functionalized silica crystals TNT concentrations (M) SiO2

—NH2

10-12

10-10

10-8

10-6

10-4

neff

1.413

1.413

1.419

1.421

1.422

1.424

1.427

ε

1.997

1.997

2.015

2.021

2.023

2.026

2.036

Since DNT crystal structures are randomized, measuring their centre-to-centre distances and hence, their neff was difficult. On the other hand, TNT functionalization produces neff


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changed after attachment of 10-12 M. In order to understand the experimental TPBES responses from 10-12 M and 10-4 M, we run a simulation by utilizing the (a) and neff of 10-12 M TNT as baseline with ao of 263.1 nm and dielectric constant of ε0 = neff2 = 1.4192 ~ 2.015. COMSOL Multiphysics 5.1 (RF module) was used to simulate the transmission spectra in the 200-800 nm range. Two sets of simulations were performed: the first set involved a parametric sweep of the centre-to-centre distance (a) of TNT functionalized crystals varying from 263.1 nm to 270. 9 nm, demonstrated in Table 1, with ε0 as 2.015, taking the 10-12 M dielectric constant presented in from Table 2. The second set involved a parametric sweep of the dielectric constant from 2.015 to 2.036, with ao as 263.1 nm. The results of the first and second simulations are displayed in Figure 10 (a) and (b), respectively. Insets of Figure 10 (a) and (b) show shifts in both variations but larger photonic bands shift (marked as 1, 2 and 3) are observed in sweeping centre-to-centre distance than the dielectric constants. Thus, the TPBES response is more sensitive to the centreto-centre distance changed than the contrast of the dielectric constant. From the simulation results, we used the photonic band (PB) edge data to compare with our experimental results.

1 PBG

0.9

0.5


0.8 0.6

2 3

1 E2

0.9

E2'

PBG

E1'

E1

0.8

0.4

E3

E3'

1.0

0.3 0.2 0.2

E1'

E1

Normalized Frequency

0.4

0.6 0.8 1.0 1.2 Normalized Frequency

1.4

1.1

(b)

1.0

2.015

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PBG

1

E1

0.8

E1'

1

1.0

0.7 0.6 0.5 0.4

E2

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2

E2'

PBG

1

3

E1'

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E1

E3

E3'

0.6 Normalized Frequency

0.3 0.2 0.2

2.021 2.023 2.026 2.036

PBG


1.0

0.7

263.1 nm 265.4 nm 266.0 nm 267.2 nm 270.9 nm

(a)

Normalized Transmittance

1.1 Normalized Transmittance

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0.4 0.6 0.8 Normalized Frequency

1.0

Figure 10. Simulation results of 3D electromagnetic waves in the frequency domains (ewfd) demonstrate (a) centre-to-centre distance variations from 263.1 nm to 270. 9 nm, keeping dielectric constant of ε0 as 2.015, whilst (b) dielectric constant variation from 2.015 to 2.036, keeping ao as 263.1 nm. Photonic band (PB) regions are labeled as 1, 2, and 3 of transmittance peaks.

We extracted the PB information from Figure 10 (a) and (b) and plotted in Figure 11 (a) and (b), respectively. Sweeping (a) produces a positive linear slope of in contrast to negative slope of varying the ε.


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(b)

(a) ε0 = 2.015 E3' E3

1.2

E2' 1.1 E2 E1'

1.0

E1 0.9 262


1.0 1.3


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ao= 263.1 nm E3'

0.9

E3

0.8

E2' E2 E1'

0.7

E1

0.6 264

266

268

270

272

2.015 2.020 2.025 2.030 2.035 2.040

Dielectric constant, ε

Centre-to-Centre distance, a (nm)

Figure 11. 3D simulation spectroscopy results: The parametric sweep of (a) centre-to-centre distance, (a) with ε0 of 2.015, and (b) dielectric constant, with ao as 263.1 nm.

Therefore, the centre-to-centre distance and dielectric constant perturbations yield a TPBES response in terms of the (a) and (ε) sweeps as shown in Equation (1): ∆ ∆ ! + ∗ ! 1 , = , + ∗

where , is the baseline band edge of 10-12 M TNT functionalized crystals, = ∗

and = ∗ are the slopes from the parametric sweep of centre-to-centre and dielectric

obtained in Figure 11 (a) and (b), respectively multiplied with their corresponding baseline

slopes of and . The shifts for different TNT concentrations in terms of the centre-to-centre distance and dielectric changed are ∆ = − and ∆ε = − , respectively. and

correspond to the centre-to-centre distance and dielectric constant of TNT concentrations where n is the concentration. Respective baseline band edges, slope values of and are

listed in Table 3. Table 3. Baseline band edges, and slope values for each parametric sweeps from the simulation results. Band edges

E a , ε

α(

β(

E1

0.3506

1.03925

-0.31837


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E1’

0.3901

1.13396

-0.44129

E2

0.4318

1.26814

-0.52592

E2’

0.5000

1.38391

-0.49771

E3

0.6283

1.34181

-0.44532

E3’

0.7149

1.35233

-0.40502

Simulation data listed in Table 3 was used to plot the TPBES responses based on Equation (1) and displayed in Figure 12. The resultant plot is a third-order polynomial fit of , as described in Equation (2):

∆ ∆ ∆ ∆ ∆ ∆ , + ∗ * !, !+ + ∗ * !, !+ + ∗ * !, !+ 2 E1'

0.40 0.38 E1 0.36 0.34 10-14 10-12 10-10 10-8 10-6 10-4 10-2 Concentration of TNT (M)



E2'

0.52 0.50 0.48 E2

0.46 0.44

0.42 10-14 10-12 10-10 10-8 10-6 10-4 10-2 Concentration of TNT (M)


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0.74

E3'

0.72 0.70 0.68 0.66

E3

0.64 0.62 10-14 10-12 10-10 10-8 10-6 10-4 10-2 Concentration of TNT (M)

Figure 12. Photonic band edges based on simulation results.

Discussion


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We have shown that the simulation results in Figure 12 are in agreement with the experimental results displayed in Figure 7 (a). The advantage of TPBES over the reflection-based results include distinctive sharp edges of photonic bands and full penetration of light through the assembled structures for the bulk properties. The measured TPBES response showed the photonic band edge shifting towards high energy in three stages for different TNT concentrations: a) 1.2-1.6% for 10-12 to 10-10 M, b) ?7@5 = 1 − 0.524 = 0.476. Thus the total volume fraction (8;@>75 ) of functionalized crystals is equivalent to 0.524 as described in Equation (4). Amine functionalization resulted in a constant volume fraction, 89:40 = 0.045 for all TNT concentrations. 0.524 = 8345467 + 89:40 + 8;

Using Transmissive Photonic Band Edge Shift to Detect Explosives: A

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